References of "Esser, Céline"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailA multifractal formalism for non-concave and non-increasing spectra: the leaders profile method
Esser, Céline ULg; Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

in Applied & Computational Harmonic Analysis (in press)

We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We show ... [more ▼]

We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We show both from the theoretical and from the applied points of view that this approach is more e cient than the wavelet-based multifractal formalisms previously introduced. [less ▲]

Detailed reference viewed: 92 (23 ULg)
Full Text
See detailDivergence of wavelet series: A multifractal analysis
Esser, Céline ULg; Jaffard, Stéphane ULg

E-print/Working paper (2017)

We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs ... [more ▼]

We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence occurs, and we show that these bounds are generically optimal, according to several notions of genericity. [less ▲]

Detailed reference viewed: 11 (1 ULg)
Full Text
See detailWavelet series representations for pathwise Young integrals
Esser, Céline ULg

Conference (2016, October)

Detailed reference viewed: 12 (1 ULg)
Full Text
See detailPropriétés multifractales de la divergence de séries d’ondelettes
Esser, Céline ULg

Conference (2016, September 22)

Dans cet exposé, nous nous intéressons à la divergence ponctuelle de séries d'ondelettes dans un espace de Besov donné. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des ... [more ▼]

Dans cet exposé, nous nous intéressons à la divergence ponctuelle de séries d'ondelettes dans un espace de Besov donné. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des points ayant un taux de divergence donné, et nous montrons que cette borne est optimale en utilisant les notions de résidualité et de prévalence. [less ▲]

Detailed reference viewed: 8 (2 ULg)
Full Text
See detailMultifractal analysis of the divergence of wavelet series
Esser, Céline ULg

Conference (2016, June 07)

In this talk, we study pointwise divergence properties of wavelet expansions of functions in a given Besov space. We obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points ... [more ▼]

In this talk, we study pointwise divergence properties of wavelet expansions of functions in a given Besov space. We obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence is observed, and we show that these bounds are generically (in the sense of Baire's categories) optimal. This gives a complement to the works done by F. Bayart and Y. Heurteaux in the case of Fourier series and by J.M. Aubry. [less ▲]

Detailed reference viewed: 22 (4 ULg)
Full Text
See detailReprésentation d'intégrales stochastiques via la base de Haar
Esser, Céline ULg

Conference (2016, May 24)

Detailed reference viewed: 16 (2 ULg)
Full Text
See detailAnalyse multifractale de la vitesse de divergence de séries d'ondelettes
Esser, Céline ULg

Scientific conference (2016, May 13)

Detailed reference viewed: 10 (0 ULg)
Full Text
See detailAlmost sure approximations in H older norms of a general stochastic process de ned by a Young integral
Ayache, Antoine; Esser, Céline ULg; Qidi, Peng

E-print/Working paper (2016)

We focus on a stochastic process $\{Y(t)\}_{t\in [0,v]}$ defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of $\{Y(t)\}_{t ... [more ▼]

We focus on a stochastic process $\{Y(t)\}_{t\in [0,v]}$ defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of $\{Y(t)\}_{t\in [0,v]}$ through Euler scheme and Riemann-Stieltjes sums with a new approach consisting in the use of an appropriate series representation of $\{Y(t)\}_{t\in [0,v]}$. This representation is obtained through a general compactly supported orthonormal wavelet basis. An advantage offered by the new approach with respect to the classical one is that a better almost sure rate of convergence in H\"older norms can be derived, under a general Gaussian condition. Also, this improved rate turns out to be optimal in some situations; typically, when the integrator associated to $\{Y(t)\}_{t\in [0,v]}$ is a fractional Brownian motion of an arbitrary Hurst parameter, and the integrand is a deterministic nowhere vanishing function with an invariant H\"older regularity large enough. [less ▲]

Detailed reference viewed: 18 (1 ULg)
Full Text
Peer Reviewed
See detailLarge deviation spectra based on wavelet leaders
Bastin, Françoise ULg; Esser, Céline ULg; Jaffard, Stéphane ULg

in Revista Matemática Iberoamericana (2016), 32(3), 859-890

We introduce a new multifractal formalism, based on distributions of wavelet leaders, which allows to detect non-concave and decreasing multifractal spectra, and we investigate the properties of the ... [more ▼]

We introduce a new multifractal formalism, based on distributions of wavelet leaders, which allows to detect non-concave and decreasing multifractal spectra, and we investigate the properties of the associated function spaces. [less ▲]

Detailed reference viewed: 153 (17 ULg)
Full Text
See detailA useful result related with zeros of continuous compactly supported mother wavelets
Ayache, Antoine; Esser, Céline ULg

E-print/Working paper (2016)

In the last two decades, wavelet bases and associated methodologies have become quite important in many domains, such as signal and image processing, harmonic analysis, statistics, and so on. More ... [more ▼]

In the last two decades, wavelet bases and associated methodologies have become quite important in many domains, such as signal and image processing, harmonic analysis, statistics, and so on. More recently, they also turn out to be quite useful in the probabilistic framework of stochastic processes, in which, among other things, they allow to obtain fine results concerning erratic sample paths behavior. The goal of our article is to derive a result, related with zeros of continuous compactly supported mother wavelets, which is useful in this probabilistic framework. More precisely, let $\psi$ be any arbitrary such wavelet; we show that being given an arbitrary point $x_0\in\R$ there always exists at least one integer $k_{x_0}\in\Z$ such that $\psi(x_0-k_{x_0}) \neq 0$. [less ▲]

Detailed reference viewed: 22 (4 ULg)
Full Text
See detailEstimation de spectres de singularités par des méthodes de grandes déviations basées sur les ondelettes
Esser, Céline ULg

Scientific conference (2015, December 02)

La régularité d'un signal en un point peut être caractérisée par son exposant de Hölder. Une description synthétique de la répartition des différents exposants de Hölder d'un signal est fournie par son ... [more ▼]

La régularité d'un signal en un point peut être caractérisée par son exposant de Hölder. Une description synthétique de la répartition des différents exposants de Hölder d'un signal est fournie par son spectre de singularités. Plusieurs méthodes basées sur la décomposition en ondelettes ont été proposées pour estimer le spectre de singularités d'un signal; elles reposent sur une caractérisation de l'exposant de Hölder par les coefficients d'ondelettes. Dans cet exposé, nous présentons une nouvelle méthode reposant sur des estimations de grandes déviations basées sur les coefficients d'ondelettes et montrons son efficacité sur plusieurs exemples déterministes ou non. [less ▲]

Detailed reference viewed: 9 (4 ULg)
Full Text
Peer Reviewed
See detailEstimation de spectres de singularités par des techniques de grandes déviations basées sur les ondelettes
Esser, Céline ULg

Conference (2015, November 26)

La régularité en un point d'une fonction peut être caractérisée par son exposant de Hölder. Si la fonction est très irrégulière, celui-ci peut varier fortement d'un point à l'autre. Dans ce cas, il est ... [more ▼]

La régularité en un point d'une fonction peut être caractérisée par son exposant de Hölder. Si la fonction est très irrégulière, celui-ci peut varier fortement d'un point à l'autre. Dans ce cas, il est naturel d'étudier la distribution des exposants de Hölder: cette information est donnée par le spectre de singularités de la fonction. En général, ce spectre est assez difficile à calculer et on utilise des méthodes pour l'estimer. Plusieurs méthodes basées sur la décomposition en ondelettes ont été proposées ; elles reposent sur une caractérisation de l'exposant de Hölder par les coefficients d'ondelettes. Dans cet exposé, nous introduisons une nouvelle technique reposant sur des estimations de grandes déviations basées sur les coefficients d'ondelettes et montrons son efficacité sur plusieurs exemples [less ▲]

Detailed reference viewed: 20 (0 ULg)
Full Text
See detailAnalyse multifractale de la divergence de séries d'ondelettes
Esser, Céline ULg

Scientific conference (2015, November 06)

Dans cet exposé, nous étudions la divergence ponctuelle de séries d'ondelettes dans un espace de Besov. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des points ayant un ... [more ▼]

Dans cet exposé, nous étudions la divergence ponctuelle de séries d'ondelettes dans un espace de Besov. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des points ayant un taux de divergence donné, et nous montrons que cette borne est optimale en utilisant les notions de résidualité et de prévalence. Il s'agit d'un travail en collaboration avec S. Jaffard. [less ▲]

Detailed reference viewed: 4 (0 ULg)
Full Text
Peer Reviewed
See detailA propos des fonctions continues qui ne sont dérivables en aucun point
Esser, Céline ULg

in Notes de la huitième Brussels Summer School of Mathematics (2015, August 03)

En 1872, Karl Weierstrass présenta non seulement une, mais toute une famille de fonctions continues et nulle part dérivables. Après la publication de ce résultat, beaucoup d'autres mathématiciens ... [more ▼]

En 1872, Karl Weierstrass présenta non seulement une, mais toute une famille de fonctions continues et nulle part dérivables. Après la publication de ce résultat, beaucoup d'autres mathématiciens apportèrent leur propre contribution en construisant d'autres fonctions continues et nulle part dérivables. Dans cet exposé, nous présenterons les fonctions de Weierstrass et nous montrerons que le théorème de Baire permet d'affirmer que l'ensemble des fonctions nulle part dérivables est dense dans l'ensemble des fonctions continues. Nous étudierons également la régularité ponctuelle des fonctions de Weierstrass en introduisant la notion d'exposant de Hölder. [less ▲]

Detailed reference viewed: 53 (8 ULg)
Full Text
See detailDenjoy-Carleman classes and lineability
Esser, Céline ULg

Conference (2015, June 16)

The Denjoy-Carleman classes are spaces of smooth functions which satisfy growth conditions on their derivatives defined through weight sequences. In this talk, given a Denjoy-Carleman class E of Beurling ... [more ▼]

The Denjoy-Carleman classes are spaces of smooth functions which satisfy growth conditions on their derivatives defined through weight sequences. In this talk, given a Denjoy-Carleman class E of Beurling type that strictly contains another non-quasianalytic class F of Roumieu type, we handle the question of knowing how large the set of functions in E that are nowhere in the class F is. In particular, we prove the dense-lineability of the set of functions of E which are nowhere in F. Consequences for the Gevrey classes are also given. We extend then these results to the case of classes of ultradifferentiable functions defined using weight functions. [less ▲]

Detailed reference viewed: 35 (4 ULg)
Full Text
See detailDense-lineability in classes of ultradifferentiable functions
Esser, Céline ULg

Conference (2015, May 27)

The Denjoy-Carleman classes are spaces of smooth functions which satisfy growth conditions on their derivatives defined through weight sequences. In this talk, given a Denjoy-Carleman class E of Beurling ... [more ▼]

The Denjoy-Carleman classes are spaces of smooth functions which satisfy growth conditions on their derivatives defined through weight sequences. In this talk, given a Denjoy-Carleman class E of Beurling type that strictly contains another non-quasianalytic class F of Roumieu type, we handle the question of knowing how large the set of functions in E that are nowhere in the class $F$ is. In particular, we prove the dense-lineability of the set of functions of $E$ which are nowhere in F. Consequences for the Gevrey classes are also given. We extend then these results to the case of classes of ultradifferentiable functions defined imposing conditions on their Fourier Laplace transform using weight functions. [less ▲]

Detailed reference viewed: 23 (3 ULg)
Full Text
See detailA propos des fonctions continues nulle part dérivables
Esser, Céline ULg

Conference (2015, February 24)

En 1872, Karl Weierstrass choqua la communauté mathématique en présentant une famille de fonctions continues nulle part dérivables. Après la publication de ce résultat, beaucoup d'autres mathématiciens ... [more ▼]

En 1872, Karl Weierstrass choqua la communauté mathématique en présentant une famille de fonctions continues nulle part dérivables. Après la publication de ce résultat, beaucoup d'autres mathématiciens apportèrent leur propre contribution en construisant d'autres fonctions continues et nulle part dérivables. Dans cet exposé, nous présenterons les fonctions de Weierstrass. De plus, nous montrerons que le th eorème de Baire permet d'affirmer que l'ensemble des fonctions nulle part dérivables est dense dans l'ensemble des fonctions continues. Nous étudierons également la régularité ponctuelle de telles fonctions en utilisant la notion d'exposant de Hölder. [less ▲]

Detailed reference viewed: 30 (3 ULg)
Full Text
Peer Reviewed
See detailAlgebrability and nowhere Gevrey differentiability
Bastin, Françoise ULg; Conejero, J. Alberto; Esser, Céline ULg et al

in Israel Journal of Mathematics (2015), 205

We show that there exist c-generated algebras (and dense in C^infty([0,1])) every nonzero element of which is a nowhere Gevrey diff erentiable function. This leads to results of dense algebrability (and ... [more ▼]

We show that there exist c-generated algebras (and dense in C^infty([0,1])) every nonzero element of which is a nowhere Gevrey diff erentiable function. This leads to results of dense algebrability (and, therefore, lineability) of functions enjoying this property. In the process of proving these results we also provide a new construction of nowhere Gevrey di fferentiable functions. [less ▲]

Detailed reference viewed: 155 (44 ULg)
Full Text
Peer Reviewed
See detailTopology on new sequence spaces defined with wavelet leaders
Bastin, Françoise ULg; Esser, Céline ULg; Simons, Laurent ULg

in Journal of Mathematical Analysis and Applications (2015), 431(1), 317-341

Using wavelet leaders instead of wavelet coefficients, new sequence spaces of type Sν are defined and endowed with a natural topology. Some classical topological properties are then studied; in particular ... [more ▼]

Using wavelet leaders instead of wavelet coefficients, new sequence spaces of type Sν are defined and endowed with a natural topology. Some classical topological properties are then studied; in particular, a generic result about the asymptotic repartition of the wavelet leaders of a sequence in Lν is obtained. Eventually, comparisons and links with Oscillation spaces are also presented as well as with Sν spaces. [less ▲]

Detailed reference viewed: 72 (27 ULg)
Full Text
See detailLacunary wavelet series on Cantor sets
Esser, Céline ULg

E-print/Working paper (2015)

We construct functions with prescribed multifractal spectra which satisfy the leaders profile method.

Detailed reference viewed: 17 (1 ULg)